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MGMAT coordinate square

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MGMAT coordinate square

by nafiul9090 » Sun Sep 11, 2011 10:00 am
A certain square is to be drawn on a coordinate plane. One of the vertices must be on the origin, and the square is to have an area of 100. If all coordinates of the vertices must be integers, how many different ways can this square be drawn?

A)4
B)6
C)8
D)10
E)12

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by cans » Sun Sep 11, 2011 10:07 am
is OA A
If yes, area=100 means side=10. thus 4 squares can be drawn in each quadrant with integer vertices...
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by nafiul9090 » Sun Sep 11, 2011 10:15 am
cans wrote:is OA A
If yes, area=100 means side=10. thus 4 squares can be drawn in each quadrant with integer vertices...
i also picked option A....but the OA is E

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by shankar.ashwin » Sun Sep 11, 2011 10:29 am
You need to understand that the distance from the origin to a point P(x,y) should be 10 for the side of a square to be 10.

The square could be of any orientation. And it also helps to know 6,8 and 10 are Pythagorus triplets, so to satisfy the condition P(x,y) could take any value such that distance from origin is 10.

You get

1) (0,10)
2 (10,0)
3) (8,6)
4) (6,8)
5) ( -6,8)
6) (8,-6)
7) (0,-10)
8) (-10,0)
9) (-6,-8)
10) (-8,-6)
11) (6,-8)
12) (-8,6)

All these are the 2nd vertices from which the square could be completed.
nafiul9090 wrote:A certain square is to be drawn on a coordinate plane. One of the vertices must be on the origin, and the square is to have an area of 100. If all coordinates of the vertices must be integers, how many different ways can this square be drawn?

A)4
B)6
C)8
D)10
E)12

how to solve this question in a short-cut way
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